Papers by Athanase Polymenis
Research journal of pharmacy and technology, Apr 22, 2024
Communications in Mathematics and Applications, Sep 30, 2021
Advances and Applications in Statistics, 2022
How to cite this article: Athanase Polymenis, Implementation of a validity test associated with t... more How to cite this article: Athanase Polymenis, Implementation of a validity test associated with the stochastic EM algorithm in mixture analysis, Advances and Applications in Statistics 74 (2022), 129-144.
International Journal of Statistics and Systems, 2017
The present article aims at applying statistical techniques for dealing with reliability issues u... more The present article aims at applying statistical techniques for dealing with reliability issues using an experiment from the aerospace industry area. To this end failure data from this area are recorded and they are classified into two distinct categories, where the category of interest is that concerning failures occurring on components that will have to be replaced in order to fix the technical problems. A Weibull distribution is then proposed, that is based upon a non-parametric approach (the so-called Median Rank) for estimating cumulative distribution functions (c. d. f.), in order to model lifetime data from the category of interest and some practical results are provided on the basis of two simple examples.
Let us consider a multivariate model which consists of a system of p equations where each equatio... more Let us consider a multivariate model which consists of a system of p equations where each equation is an AR(1) process taking the form X , X , s ε , , for k 1 >0, and ε , ~N 0,1 . Also consider that vector satisfies the equation X X sε X , , ... , X , ′ and ε ~N 0 , I are serially independent random vectors (where 0 is the vector with all components equal to 0, the pxp identity matrix, and s is a diagonal positive entries so that the vector components of independent random variables). We call this model Multivariate Model 1. It is obvious that, for any
The aim of the present study is to evaluate the performance of the Stochastic EM (SEM) algorithm ... more The aim of the present study is to evaluate the performance of the Stochastic EM (SEM) algorithm for estimating parameters in finite mixture distributions. For that purpose some simulation exercises which are based on the implementation of this algorithm are presented and they provide encouraging results. As a consequence it seems that SEM can offer a useful alternative for overcoming some well-known difficulties arising when the number of mixture components is itself an unknown parameter.
Neutrosophic statistics are used when one is dealing with imprecise and indeterminate data or par... more Neutrosophic statistics are used when one is dealing with imprecise and indeterminate data or parameters. In the present paper we propose a method for performing a neutrosophic Student’s t –type of statistical test that concerns the population mean when data arise from an autoregressive process of order 1 (AR(1)). In classical statistics data obtained through this process are not independent when the autocorrelation coefficient of the process is not equal to 0, and hence the usual Student’s t distribution is inadequate for inferring about the population mean; however a result obtained in earlier literature states that a Student’s t –type of statistic, which is asymptotically normally distributed, can be used instead. Our method is based on the neutrosophic version of this result and it is implemented using simulated data.
International journal of applied mathematics and statistics, 2019
Information-based methods have been found useful for providing alternative ways in order to addre... more Information-based methods have been found useful for providing alternative ways in order to address the difficult problem of estimating the number of components in finite mixture models. In the present study we focus on a specific information-based method called minimum information ratio (MIR) criterion. Since simulation results presented in earlier research work showed in general a nice performance of this criterion in cases of good data clustering the aim of the present study will be to investigate reasons underlying such behavior. Our approach is motivated by the fact that a high MIR value computed during implementation of this criterion when a model with true number of components k is fitted can be considered as a natural indicator for good data clustering, whereas a small MIR value indicates poor data clustering. Simulations show that the more data clustering is improved the more the magnitude of this indicator exceeds corresponding magnitudes of MIR values obtained from fitted...
Asian Journal of Medical Sciences, 2021
Background: COVID-19 disease has quickly become a pandemic because of high infectiousness among p... more Background: COVID-19 disease has quickly become a pandemic because of high infectiousness among populations. In order to assess for infectiousness reproduction numbers have been widely used in existing literature. A recent research has estimated reproduction numbers by location in order to account for differences among infectiousness. Aims and Objective: The aim of the present work was to use reproduction numbers in order to obtain an estimate for the mean number of contacts of some patient up to the first transmission of the disease to some other person in a specific location. The objective is to help authorities collect even more information on disease transmission. Materials and Methods: Our study was based on results obtained in a recent research work where replicated values of reproduction numbers have been generated in order to estimate medians and 95% confidence intervals for these numbers and thus assess infectiousness. We proposed a method that relies on a geometric distrib...
Journal of Population Therapeutics and Clinical Pharmacology, 2020
In the present study, we are interested in modeling repose time periods (the length of the time i... more In the present study, we are interested in modeling repose time periods (the length of the time intervals between successive deaths) caused by a new, widespread disease called covid-19. This is useful for predicting probabilities of new deaths that occur within pre-determined time intervals. In practical applications, the choice of the statistical model is crucial for obtaining accurate estimates of death hazard rates. Based on an earlier research, we propose to use a mixture of exponential distributions; this model is simple to implement when hazard rates obtained from the components of the mixture are easily calculated, and it is adequate for dealing with nonstationary time series as those appearing in the case of this disease. The model is then applied to the example of Italy, and it appears to be also useful for comparing hazard rates along time.
Journal of Statistics and Management Systems, 2018
To cite this article: Athanase Polymenis (2018) Asymptotic results for a stationary random proces... more To cite this article: Athanase Polymenis (2018) Asymptotic results for a stationary random process generated by the stochastic EM algorithm in mixture analyses,
Advances and Applications in Statistics, 2019
International Journal of Advanced Mathematics and Statistics, 2016
In the present article the multivariate central limit theorem is revisited. Rather than simply re... more In the present article the multivariate central limit theorem is revisited. Rather than simply reviewing existing methodology our approach mostly aims at giving particular emphasis on some univariate techniques that support the proof of this theorem. On those grounds all necessary mathematical arguments are duly provided.
All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is d e p e n d e n ... more All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is d e p e n d e n t upon the quality of the copy subm itted. In the unlikely e v e n t that the a u thor did not send a c o m p le te m anuscript and there are missing pages, these will be noted. Also, if m aterial had to be rem oved, a n o te will ind ica te the deletion.
Statistics & Probability Letters, 1998
A modification is proposed to a method of Windham and Cutler (1992) for determining the number of... more A modification is proposed to a method of Windham and Cutler (1992) for determining the number of components in a mixture. An information-based eigenvalue is computed that, in theory, becomes zero as soon as too many mixture components are included in the model. In a simulation exercise, the method appears to out-perform the basic method of Windham and Cutler (1992),
Journal of Statistical Computation and Simulation, 1999
Goffinet et al. (1992) derived the limiting distribution of the likelihood ratio test statistic (... more Goffinet et al. (1992) derived the limiting distribution of the likelihood ratio test statistic (LRTS) when testing between a normal distribution and a mixture of two normal distributions with known proportion p. This distribution depends discontinuously on values of p.. Simulations performed by the above authors have shown a very slow convergence towards the theoretical results in the case that p. is close to 0.5. In this paper we shall study the distribution of the LRTS for reasonable sample sizes, and give a heuristic explanation that accounts for the slow convergence.
Journal of Mathematics and Statistics, 2011
Problem statement: Hotelling's T 2 statistic has been well documented in the existing literature ... more Problem statement: Hotelling's T 2 statistic has been well documented in the existing literature and exact as well as asymptotic results have been obtained. In the present article, we focus on an important particular case of T 2 and we note that, there is no clear way to show, how univariate results, used in the theory of Student's t statistic, could be used to derive corresponding multivariate ones, for T 2. Therefore, our goal is to find an alternative method, which would be more useful than the usual one, in order to generalize directly univariate theory. Approach: At first, we used some matrix tools in order to obtain an equivalent algebraic form for T 2 and, then, we applied some univariate results concerning distributions which arise from the normal distribution. Results: We found an algebraic representation of T 2 , which can be conceived as the natural extension of some results appearing in the literature and, we used our findings to show how standard univariate techniques can be applied in order to derive the exact and limiting distributions of T 2. Conclusion: Using the proposed representation of T 2 gives a better insight on the generalization of univariate results to multivariate analyses and indicates, at the same time, an alternative way to prove typical multivariate results. Furthermore, it allows for usual theoretical calculations to simplify.
Computational Statistics & Data Analysis, 2014
Modified MIR is a Monte-Carlo algorithm used for bootstrapping minimum information ratios in orde... more Modified MIR is a Monte-Carlo algorithm used for bootstrapping minimum information ratios in order to assess the number of unknown components in finite mixtures. The method was proposed as a modification of the minimum information ratio (MIR) method, and was proved to outperform it. Further simulations and a comparison with some other approaches confirm that the method works well for reasonable sample sizes. However, an important drawback which occurs with information ratio driven methods is that they do not allow for testing for the hypothesis of a single-component model. In order to overcome this problem, a combined method is proposed which consists of including a bootstrap likelihood ratio step and a modified MIR step into a single programming package. The bootstrap likelihood ratio methods show in general nice performances, so the combined method is also expected to be adequate for detecting single-component models. This, in turn, implies that the performance of the method is expected to be very similar to that of modified MIR in situations where the model is a true mixture. A simulation exercise is carried out, which confirms this feeling. This result is then in support of using the combined method rather than modified MIR for practical applications.
Uploads
Papers by Athanase Polymenis